In the manufacture of plywood panels or laminated veneer lumber (LVL), the veneers are laid up at a lay-up station for a veneer assembly with a thickness of several veneer layers. Top surfaces of the veneers have adhesive applied thereto and the veneers are laid on top of each other and then, in the next working step, brought to a permanent attachment with each other by the application of pressure and heat. This calls for a precise alignment of veneers relative to each other. Traditionally, the alignment has been performed manually against two stationary fences. At present, the lay-up operation is often machine-operated, but two stationary fences are still involved one way or another. The manufacture of LVL has involved the use of a mechanical lay-up operation. However, the LVL is structurally different with its veneers supposedly parallel to each other. The application publication US 2003/0173734 describes one LVL manufacturing apparatus and method, enabling a precise alignment of veneer sheets relative to each other by adapting what in the advancing direction of a veneer sheet constitutes its leading edge to function as an alignment edge and by positioning the veneer sheets at a lay-up station on top of a two-segment tablet arrangement, said tablet segments being adapted to move towards and away from each other. In this solution, the identification of a leading edge position is used as a controlling parameter for the process. Still, even in this solution, the leading edge is identified by mechanical brackets in just two positions.